Question

Select the polynomial that has (x-3) as a factor A) p(x) =x³-2x²-4x+3B) p(x) =x⁴-20x-23C) p (x) =x⁴-2x³-25D) p (x) =x³+3x²-2x-6

Answer 1

We will use the theorem of remainder to solve the question

Equate x - 3 by 0 to find x

x - 3 = 0

Add 3 to both sides

x - 3 + 3 = 0 + 3

x = 3

Now substitute x by 3 in the polynomial if the answer = 0, then x - 3 is a factor of it

Let start with the first answer

$\begin{gathered} p(3)=(3)^3-2(3)^2-4(3)+3 \\ p(3)=27-18-12+3=0 \end{gathered}$

Then (x - 3) is a factor of it

The answer is A